A monophonic set ???? of a connected graph ???? is said to be a non split monophonic set if ???? = ???? (????) or the subgraph ⟨???? − ????⟩ is connected. The minimum cardinality of the non split monophonic set is the non split monophonic number of ???? and is denoted by ????????????(????). In this paper we have characterised the non split monophonic sets of the join and corona of two graphs. Also, we have calculated the non split monophonic number of the join and corona product of two graphs.